A prediction for three neutrino masses and mixings and similarity between quark and lepton mixings

Abstract

If neutrinos have mass, we give reasons for a possible pattern of three (squared) mass eigenvalues: $m_1^2 \simeq (2.8 - 5.8) \, \mbox{(eV)}^2 $, $m_2^2 \simeq 0.01 \, \mbox{(eV)}^2 $, $m_3^2 \simeq (1.5 - 1) \times 10^{-4} \mbox{(eV)}^2 $. The flavor states $\nu_{\mu} $ and $\nu_e $ are mixtures of the eigen\-states with $m_2 $ and $m_3 $ with a significant mixing, corresponding to an effective mixing angle of about 0.45. The $\nu_{\tau} $ is nearly the state with $m_1 $; the other two effective mixing angles are about an order of magnitude smaller than 0.45. There is a marked similarity to mixing in the quark sector.